Joining polynomial and exponential combinatorics for some entire maps

We consider families of entire transcendental maps given by Fλ,m(z) = λzm exp(z) where m ≥ 2. All these maps have a superattracting fixed point at z = 0 and a free critical point at z = −m. In parameter planes we focus on the capture zones, i.e., we consider λ values for which the free critical poin...

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Detalles Bibliográficos
Autores: Garijo Real, Antonio, Jarque i Ribera, Xavier, Moreno Rocha, Mónica
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2010
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/132422
Acceso en línea:https://hdl.handle.net/2445/132422
Access Level:acceso abierto
Palabra clave:Anàlisi combinatòria
Sistemes dinàmics diferenciables
Combinatorial analysis
Differentiable dynamical systems
Descripción
Sumario:We consider families of entire transcendental maps given by Fλ,m(z) = λzm exp(z) where m ≥ 2. All these maps have a superattracting fixed point at z = 0 and a free critical point at z = −m. In parameter planes we focus on the capture zones, i.e., we consider λ values for which the free critical point belongs to the basin of attraction of z = 0. We explain the connection between the dynamics near zero and the dynamics near infinity at the boundary of the immediate basin of attraction of the origin, thus, joining together exponential and polynomial behaviors in the same dynamical plane.